Compensation of Non-Linear Transmitter Impairments in Optical Communication Networks

ABSTRACT

An optical transceiver comprises a transmitter configured to transmit a first signal, and a receiver coupled to the transmitter and configured to receive a first compensation, wherein the first compensation is based on a pattern-dependent analysis of the first signal, and provide the first compensation to the transmitter, wherein the transmitter is further configured to compensate a second signal based on the first compensation to form a first compensated signal, and transmit the first compensated signal. An optical transmitter comprises a digital signal processor (DSP) comprising a compensator, a digital-to-analog converter (DAC) coupled to the DSP, a radio frequency amplifier (REA) coupled to the DAC, and an electrical-to-optical converter (EOC) coupled to the REA. An optical receiver comprises an optical-to-electrical converter (OEC), an analog-to-digital converter (ADC) coupled to the OEC, and a digital signal processor (DSP) coupled to the ADC and comprising a calibrator.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of U.S. patent applicationSer. No. 14/341,373 filed on Jul. 25, 2014 by Clarence Kan, et al., andtitled “Compensation of Non-Linear Transmitter Impairments in OpticalCommunication Networks,” which is incorporated by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

REFERENCE TO A MICROFICHE APPENDIX

Not applicable.

BACKGROUND

Optical communication networks serve an important function in worldwidecommunication. They have increasingly replaced copper wirecommunications due to various advantages that they offer, Opticalcommunication networks may include various nodes connected by opticalfibers or free space. As users demand higher data rates, it is becomingincreasingly important to transmit and receive optical data moreaccurately.

SUMMARY

In one embodiment, the disclosure includes an optical transceivercomprising a transmitter configured to transmit a first signal, and areceiver coupled to the transmitter and configured to receive a firstcompensation, wherein the first compensation is based on apattern-dependent analysis of the first signal, and provide the firstcompensation to the transmitter, wherein the transmitter is furtherconfigured to compensate a second signal based on the first compensationto form a first compensated signal, and transmit the first compensatedsignal.

In another embodiment, the disclosure includes an optical transmittercomprising a digital signal processor (DSP) comprising a compensator, adigital-to-analog converter (DAC) coupled to the DSP, a radio frequencyamplifier WA) coupled to the DAC, and an electrical-to-optical converter(EOC) coupled to the RFA.

In yet another embodiment, the disclosure includes an optical receivercomprising an optical-to-electrical converter (OEC), ananalog-to-digital converter (ADC) coupled to the OEC, and a digitalsignal processor (DSP) coupled to the ADC and comprising a calibrator.

In yet another embodiment, the disclosure includes a method comprisingtransmitting a first optical signal, receiving a first compensation,wherein the first compensation is based on a pattern-dependent analysisof the first optical signal, compensating a second optical signal basedon the first compensation to form a first compensated optical signal,and transmitting the first compensated optical signal.

These and other features will be more clearly understood from thefollowing detailed description taken in conjunction with theaccompanying drawings and claims,

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of this disclosure, reference is nowmade to the following brief description, taken in connection with theaccompanying drawings and detailed description, wherein like referencenumerals represent like parts.

FIG. 1 is a schematic diagram of a network device.

FIG. 2 is a schematic diagram of an optical network according to anembodiment of the disclosure.

FIG. 3 is a schematic diagram of an optical modulator according to anembodiment of the disclosure.

FIG. 4 is a schematic diagram of an optical network according to anotherembodiment of the disclosure.

FIG. 5 is a schematic diagram of the calibrator in the optical networkin FIG. 4 according to an embodiment of the disclosure.

FIG. 6 is an example of a pattern-dependent look-up table (PD-LUT)according to an embodiment of the disclosure.

FIG. 7 is a schematic diagram of the compensator in the optical networkin FIG. 4 according to an embodiment of the disclosure.

FIG. 8 is a message sequence diagram illustrating iterative calibrationand compensation scheme according to an embodiment of the disclosure.

FIG. 9 is a graph of a modeled bit error rate (BER) for the opticalnetwork in FIG. 4,

FIG. 10 is another graph of a modeled BER for the optical network inFIG. 4.

FIG. 11 is a graph of an experimental symbol constellation for theoptical network in FIG. 4.

FIG. 12 is another graph of an experimental symbol constellation for theoptical network in FIG. 4.

FIG. 13 is a graph of experimental optical signal-to-noise ratio (OSNR)versus BER for the optical network in FIG. 4.

FIG. 14 is a graph of experimental pattern length versus BER for theoptical network in FIG. 4.

FIG. 15 is a flowchart illustrating a method of transmitter impairmentcompensation according to an embodiment of the disclosure.

DETAILED DESCRIPTION

It should be understood at the outset that, although an illustrativeimplementation of one or more embodiments are provided below, thedisclosed systems and/or methods may be implemented using any number oftechniques, whether currently known or in existence. The disclosureshould in no way be limited to the illustrative implementations,drawings, and techniques illustrated below, including the exemplarydesigns and implementations illustrated and described herein, but may bemodified within the scope of the appended claims along with their fullscope of equivalents.

FIG. 1 is a schematic diagram of a network device 100. The networkdevice 100 may be suitable for implementing the disclosed embodiments.The network device 100 may comprise ingress ports 110 and receiver units(Rx) 120 for receiving data; a processor, logic unit, or centralprocessing unit (CPU) 130 to process the data; transmitter units (Tx)140 and egress ports 150 for transmitting the data; and a memory 160 forstoring the data. The network device 100 may also compriseoptical-to-electrical (OE) components and electrical-to-optical (EO)components coupled to the ingress ports 110, receiver units 120,transmitter units 140, and egress ports 150 for egress or ingress ofoptical or electrical signals.

The processor 130 may be implemented by hardware and software. Theprocessor 130 may be implemented as one or more CPU chips, cores (e.g.,as a multi-core processor) field-programmable gate arrays (FPGAs),application specific integrated circuits (ASICs), and digital signalprocessors (DSPs). The processor 130 may be in communication with theingress ports 110, receiver units 120, transmitter units 140, egressports 150, and memory 160.

The memory 160 may comprise one or more disks, tape drives, andsolid-state drives; may be used as an over-flow data storage device; maybe used to More programs when such programs are selected for execution;and may be used to store instructions and data that are read duringprogram execution. The memory 160 may be volatile and non-volatile andmay be read-only memory (ROM), random-access memory (RAM), ternarycontent-addressable memory (TCAM), and static random-access memory(SRAM).

FIG. 2 is a schematic diagram of an optical network 200, The network 200may comprise a first transceiver 205 and a second transceiver 250 incommunication with each other via a medium 245. The components of theoptical network 200 may be arranged as shown or in any other suitablemanner. Some of the components may comprise multiple inputs and multipleoutputs that may, for instance, run in parallel; however, the componentsmay be simplified for easier understanding.

As an example, the first transceiver 205 may be located in any node inan optical network and the second transceiver 250 may be located in anyother node in the optical network. Alternatively, the TX 210 and the RX255 may be part of a single transceiver in a fiber loop-backconfiguration. Furthermore, the first transceiver 205 and the secondtransceiver 250 may be located in any optical communication network,including a long-haul network, a metropolitan network, a passive opticalnetwork (PON), or another optical network using high-order modulation.

The first transceiver 205 may be any transceiver suitable fortransmitting and receiving optical signals. The first transceiver 205may comprise a transmitter (TX) 210 and a receiver (RX) 240 coupled toeach other via a coupler 235. The TX 210 may comprise modules, includinga digital signal processor (DSP) 215, a digital-to-analog converter(DAC) 220, a radio frequency amplifier (RFA) 225, and anelectrical-to-optical converter (EOC) 230. The components of the firsttransceiver 205 may be arranged as shown or in any other suitablemanner.

The medium 245 may be any medium suitable for providing communicationbetween the first transceiver 205 and the second transceiver 250. Forinstance, the medium 245 may be an optical fiber cable. in that case,the medium 245 may comprise one or more optical fibers that eachcomprises a core and a cladding layer, and the medium 245 may becontained in a tube to protect from the environment.

The second transceiver 250 may be any transceiver suitable fortransmitting and receiving optical signals. The second transceiver 250may comprise an RX 255 and a TX 280 coupled to each other via a coupler275. The RX 255 may comprise various modules, including a DSP 260, ananalog-to-digital converter (ADC) 265, and an optical-to-electricalconverter (OEC) 270. The components of the second transceiver 250 may bearranged as shown or in any other suitable manner. The first transceiver205 and the second transceiver 250 may comprise additional componentsknown in the art in order for the first transceiver 205 and the secondtransceiver 250 to communicate with each other.

The first transceiver 205 may need to transmit signals to the secondtransceiver 250. In order to generate a high-order modulation signalover an in-phase (I) and quadrature-phase (Q) optical modulator, first,the DSP 215 may form multi-level I and Q digital electrical signals andpre-condition those digital electrical signals. Second, the DAC 220 mayconvert the digital electrical signals to analog electrical signals. TheDAC 220 may have a finite resolution and frequency response. Third, theRFA 225 may amplify the analog electrical signals. The RFA. 225 may havea finite bandwidth. Fourth, the EOC 230, which may comprise aMach-Zehnder modulator, may convert the analog electrical signals intooptical signals. Fifth, the first transceiver 205 may transmit theoptical signals through the coupler 235 and the medium 245 to the secondtransceiver 250.

The second transceiver 250 may first receive the optical signals overthe medium 245 and through the coupler 275. Second, the OEC 270 mayconvert the optical signals to analog electrical signals. Third, the ADC265 may convert the analog electrical signals into digital electricalsignals. Fourth, the DSP 260 may process the digital electrical signalsas appropriate.

FIG. 3 is a schematic diagram of an optical modulator 300. The modulator300 may be a polarization-multiplexed I and Q Mach-Zehnder and may beused in the EOC 230. The modulator 300 may comprise a polarization beamsplitter (PBS) 310, a first Mach-Zehnder modulator array 320, a secondMach-Zehnder modulator array 330, and a polarization beam coupler (PBC)340. The components of the modulator 300 may be arranged as shown or inany other. suitable manner.

The PBS 310 may split a laser into an X polarization component and a Ypolarization component. The first Mach-Zehnder modulator array 320 maysplit the X polarization component into a first component and secondcomponent and modulate the first component as an X_(I) component and thesecond component as an X_(Q) component. The X_(Q) component may hevoltage-biased to have π/2 optical phase shift compared to the X_(I)component. The first Mach-Zehnder modulator array 320 may then multiplexthe X_(I) component and the X_(Q) component together to form a modulatedX component. The second Mach-Zehnder modulator array 330 may split the Ypolarization component into a first component and second component andmodulate the first component as a Y_(I) component and the secondcomponent as a Y_(Q) component. The X_(Q) component may bevoltage-biased to have π/2 optical phase shift compared to the X_(I)component. The second Mach-Zehnder modulator array 320 may thenmultiplex the Y_(I) component and the Y_(Q) component together to form amodulated Y component. Finally, the PBC 340 may couple, or multiplex,the modulated X component and the modulated Y component to form apolarization-multiplexed signal.

High-order modulation is a promising technology to achievespectrally-efficient terabit (Tb) transmission in optical networks suchas the network 200. High-order modulated. signals can be generated bymodulators such as the optical modulator 300. By modulating both the Xpolarization component and the Y polarization component, the opticalmodulator 300 may double the spectral efficiency.

Using existing approaches to pre-conditioning of the digital electricalsignals in the DSP 215 in the first transceiver 205, the signals cansubstantially deviate from the expected values due to non-linearresponses of the electrical and optical components of the TX 210 in thefirst transceiver 205. Those deviations, or impairments, may cause apoor BER at a coherent receiver such as the RX 255 in the secondtransceiver 250. A poor BER may shorten transmission distances, whichmay increase the need for signal regeneration, thus resulting in higherinfrastructure costs.

The impairments may comprise two parts, a static part that does notdepend on the data pattern and a dynamic part that does depend on thedata pattern. The dynamic part that does depend on the data pattern maybe caused by a memory effect, With application of a near-Nyquistpulse-shaping filter such as a raised-root-cosine (RRC) filter with aroll-off factor of less than 0.2, the level deviation becomesessentially pattern dependent due to filtering-induced inter-symbolinterference (ISI).

DSP techniques may at leak partially equalize, or compensate, theimpairments. At the TX 210 in the first transceiver 205, afrequency-domain equalizer (FDEQ) and a finite impulse responsepre-equalizer (FIR) may compensate linear impairments such as radiofrequency (F) bandwidth limitations or I-Q delays. At the RX 255 in thesecond transceiver 250, an FDEQ may compensate for fiber chromaticdispersion and perform frequency filtering optimization, includingbandwidth compensation. A time-domain equalizer (IDEQ) and carrierrecovery (CR) module may recover the transmitted X polarization and Ypolarization and compensate for polarization mode dispersion, andcarrier phase recovery. Those DSP techniques may not, however,compensate for non-linear, pattern-dependent impairments.

Prior approaches to compensate for non-linear, pattern-dependentimpairments include Joel L. Dawson, “Power Amplifier LinearizationTechniques: An Overview,” Feb. 4, 2001 (“Dawson”); Shawn P. Stapleton,“Presentation on Digital Predistortion of Power Amplifiers,” June 2001(“Stapleton”); Jian Hong Ke, et al., “Three-carrier 1 Tbit/s DualPolarization 16-QAM Superchannel Using Look-Up Table Correction andOptical Pulse Shaping,” Optics :Express, Vol. 22, No. 1, Jan. 13, 2014(“Ke 1”); and ham :Hong :Ke, et al., “400 Gbit/s single-carrier and 1Tbit/s three-carrier superchannel signals using dual polarization 16-QAMwith look-up table correction and optical pulse shaping,” OpticsExpress, Vol. 22, No. 1, Dec. 20, 2013 (“Ke 2”), which are incorporatedby reference. Ke 1's and Ke 2's first approach uses a digitally sampledsignal at the transmitter to generate a PD-LUT. The sampled signal isthen adjusted based on the PD-LUT to produce an equalized, orcompensated, driver amplitude. First, that approach may requireadditional hardware, including an RF splitter and an ADC at thetransmitter to acquire the sampled drive signal. Second, that approachmay result in driver power loss. Third, that approach may incorrectlycompensate intentional pre-distortion such as pulse shaping, bandwidthpre-compensation, and dispersion pre-compensation, which may be used tocompensate transmission impairments after the point where the signal issampled. Ke 1's and Ke 2's second approach generates the PD-LUT andcompensates the signal at the receiver DSP. Both approaches describe asingle iteration of calibration and compensation.

Disclosed herein are embodiments for improved compensation oftransmitter impairments. Those impairments may be non-linear,pattern-dependent impairments. The disclosed embodiments may provide forcalibration by generating a compensation, which may be a PD-LUT, basedon a pattern-dependent analysis of data received at a receiver, thenpattern-dependent level equalization (PD-LEQ) or compensation, in atransmitter based on the PD-LUT. There may be multiple iterations ofcalibration and compensation with each successive iteration providingimproved compensation. The disclosed embodiments may be suitable for anyoptical communication network, including a PON, a long-haul network, ametropolitan network, or another optical network using high-ordermodulation. The disclosed embodiments may provide at least threebenefits, First, by generating the PD-LUT based on the pattern-dependentanalysis of data received at the receiver and not the transmitter, thetransmitter may not require any additional hardware, which may reducetransmitter size and cost. Second, there may be less or no undesiredcompensation of intentional pre-distortion such as bandwidthpre-compensation, pulse shaping, and dispersion pre-compensation. Third,by calibrating in the receiver after the DSP, including after the TDEQ,then compensating in the transmitter, the impairments may he moreaccurately compensated because the data sequence is error-free and thedata patterns can be accurately determined at the transmitter. Fourth,multiple iterations of calibration and compensation may further improvecompensation and thus further reduce the BER at the receiver.

FIG. 4 is a schematic diagram of an optical network 400 according to anembodiment of the disclosure. As can be seen, the network 400 may be thesame as, and function the same as, the network 200 with a fewexceptions. First, the DSP 260 in the second transceiver 250 maycomprise an additional module, a calibrator 410. Second, the RX 255 maycommunicate with the TX 280 in the second transceiver 250 to, forinstance, provide a PD-LUT. Third, the DSP 215 in the first transceiver205 may comprise an additional module, a compensator 420. The TX 210 maynot comprise any additional signal processing modules before thecompensator 420. Fourth, the TX 210 may communicate with the RX 240 inthe first transceiver 205 to, for instance, receive the PD-LUT. Thecomponents of the optical network 400 may be arranged as shown or in anyother suitable manner.

The calibrator 410 may generate the PD-LUT, and the RX 255 may providethe PD-LUT to the TX 280. The TX 280 may transmit the PD-LUT to thefirst transceiver 205 via the coupler 275 and the medium 245. The RX 240may receive the PD-LUT via the medium 245 and the coupler 235. The RX240 may provide the PD-LUT to the TX 210, and the compensator 420 maycompensate signals in the TX 210 based on the PD-LUT. The operation ofthe calibrator 410 and the compensator 420 are described more fullybelow.

FIG. 5 is a schematic diagram of the calibrator 410 in the opticalnetwork 400 in FIG. 4 according to an embodiment of the disclosure. Thecalibrator 410 may comprise modules, including a multiple-input andmultiple-output (MIMO) TDEQ and CR module 510; a slicer 520; a patternmatcher 530; a mean calculator 540; an adjustment calculator 550; and aPD-LUT generator 560. The components of the calibrator 410 may bearranged as shown or in any other suitable manner. Some of thecomponents may comprise multiple inputs and multiple outputs that may,for instance, run in parallel; however, the components may be simplifiedfor easier understanding.

The calibrator 410 may output four PD-LUTs, one for each of an X_(I)component, an X_(Q) component, a Y_(I) component, and a Y_(Q) component.The X_(I) component may correspond to an X-polarization and I componentof a signal, the X_(Q) component may correspond to an X-polarization andQ component of the signal, the Y_(I) component may correspond to aY-polarization and component of the signal, and the Y_(Q) component maycorrespond to a Y-polarization and Q component of the signal. Thecalibrator 410 is described further below with respect to an arbitrarycomponent of the signal.

The MIMO TDEQ and CR module 510 may receive an input from the DSP 260 ofthe RX 255, The input from the DSP 260 may result from known digitalsignal processing (DSP) techniques applied in, for instance, upstreammodules of the DSP 260. The MIMO portion of the MIMO TDEQ and CR module510 may demultiplex the X and Y components of the input from the DSP260. The TDEQ portion of the MIMO TDEQ and CR module 510 may equalizelinear distortion of the signal. The CR portion of the MIMO TDEQ and CRmodule 510 may recover a phase of modulation. For instance, the signalmay have been modulated using quadrature amplitude modulation (QAM). Theoutput of the MIMO TDEQ and CR module 510 may be a soft signalcomprising the X_(I) component, the X_(Q) component, the Y_(I)component, and the Y_(Q) component. A soft signal may refer to thesignal actually received. In other words, the soft signal may resultfrom noise and distortion and thus may not correspond to the discretelevels of the modulation scheme.

The slicer 520 may compare the soft signal to the discrete levels of themodulation scheme. The slicer 520 may then convert the soft signal to ahard signal based on the comparison. A hard signal may refer to a signalwith symbols corresponding to the discrete levels of the modulationscheme.

The pattern matcher 530 may compare the hard signal to mapped levels,which may he based on an arbitrary scheme. The arbitrary scheme may havethe same number of levels as the modulation scheme, but use differentlevels. The pattern matcher 530 may then convert the hard signal to amatched signal based on the comparison. The pattern matcher 530 may alsocalculate a pattern index by multiplying the first symbol in the firstsequence of the signal by the number of matched levels raised to thepower of the symbol number, multiplying the second symbol in the firstsequence of the signal by the number of matched levels raised to thepower of the symbol number, and so on for each symbol, then adding thequantities together.

The mean calculator 540 may calculate a mean of the center symbol ofeach sequence of the soft signal. The adjustment calculator 550 maysubtract the mean from the center symbols of the hard signal to obtainthe adjustment. The center symbol for each of the sequencescorresponding to a pattern index will be the same.

Finally, the PD-LUT generator 560 may generate a PD-LUT based on thepattern index and the adjustment. The PD-LUT may further compriseadditional pattern indices with their respective adjustments. The PD-LUTgenerator 560 may similarly generate PD-LUTs for each X_(I) component,X_(Q) component, Y_(I) component, and Y_(Q) component of the signalinputted from the DSP 260. The RX 255 may provide the PD-LUTs to the TX280, and the TX 280 may transmit the PD-LUTs to the first transceiver205 via the coupler 275 and the medium 245.

As an example, the calibrator 410 may receive from the DSP 260 a signalwith sequences comprising five consecutive symbols (i.e., a patternlength of five) and modulated using 16-QAM, which may yield fourdiscrete levels (e.g., −3, −1, 1, and 3). The number of unique patternsmay therefore be 4⁵, or 1,024. The range of the pattern index maytherefore be 0-1,023 or 1-1,024. After performing its functions, theMIMO TDEQ and CR module 510 may then output the soft signal as follows:

(−3.1, −2.8, −1.2, 1.2, 3.2)

(−3.2, −2.9, −1.1, 1.4, 2.9)

(−2.9, −2.7, −0.8, 1.1, 3.1).   (1)

The slicer 520 may compare the soft signal (1) to the four discretelevels, −3 −1, 1, and 3. For instance, −3.1 in the first symbol of thefirst sequence may be closer to −3 than to any other discrete level,−2.8 in the second symbol of the first sequence may be closer to −3 thanto any other discrete level, −1.2 in the third symbol of the firstsequence may be closer to −1 than to any other discrete level, 1.2 inthe fourth symbol of the first sequence may be closer to 1 than to anyother discrete level, and 3.2 in the fifth symbol of the first sequencemay be closer to 3 than to any other discrete level. The slicer 520 maysimilarly compare the remaining sequences to obtain the following hardsignal:

(−3, −3, −1, 1, 3)

(−3, −3, −1, 1, 3)

(−3, −3, −1, 1, 3).   (2)

The pattern matcher 530 may match the hard signal (2) to a matchedsignal based on four mapped levels 0, 1, 2, and 3). The hard signal (2)may therefore become the following matched signal:

(0, 0, 1, 2, 3)

(0, 0, 1, 2, 3)

(0, 0, 1, 2, 3).   (3)

The pattern matcher 530 may also calculate the pattern index of thematched signal (3) by multiplying the first symbol in the first sequenceof the signal by the number of matched levels (i.e., 4) raised to thepower of the symbol number (i.e., 0), multiplying the second symbol inthe first sequence of the signal by the number of matched levels (i.e.,4) raised to the power of the symbol number i.e., 1), and so on for eachsymbol, then adding the quantities together as follows:

(0×4⁰)±(0×4¹)+(1×4²)+(2×4³)+(3×4⁴)=912.   (4)

The mean calculator 540 may then calculate the mean of the center (i.e.,third) symbol of each sequence of the soft signal (1) as follows:

$\begin{matrix}{\frac{\left( {- 1.2} \right) + \left( {- 1.1} \right) + \left( {- 0.8} \right)}{3} = {- {1.03.}}} & (5)\end{matrix}$

The adjustment calculator 550 may subtract the mean (5) from the centersymbol of the hard signal (2) to obtain the adjustment as follows:

(−1)−(−1.03)=0.03.   (6)

Finally, the PD-LUT generator 560 may generate a PD-LUT based on thepattern index (4), 912, and the adjustment (6), 0.03.

FIG. 6 is an example of a PD-LUT 600 according to an embodiment of thedisclosure. The PD-LUT 600 may be, for instance, a PD-LUT generated bythe PD-LUT generator 560. As shown, the PD-LUT 600 may comprise thepattern index (4), 912, and the adjustment (6), 0.03. The PD-LUT 600 mayfurther comprise, for instance, pattern indices 896 and 976 and theirrespective adjustments, 0.06 and 0.04. Finally, the PD-LUT 600 mayfurther comprise additional pattern indices and their respectiveadjustments as indicated by the ellipses. As described above, there maybe up to 1,024 unique pattern indices.

FIG. 7 is a schematic diagram of the compensator 420 in the opticalnetwork 400 in FIG. 4 according to an embodiment of the disclosure. Thecompensator 420 may comprise modules, including a pattern matcher 710,and an adjuster 720. The components of the compensator 420 may bearranged as shown or in any other suitable manner. Some of thecomponents may comprise multiple inputs and multiple outputs that may,for instance, run in parallel; however, the components may be simplifiedfor easier understanding. The compensator 420 may output an X_(I)component, an X_(Q) component, a Y-I component, and a Y_(Q) component.The compensator 420 is described further below with respect to anarbitrary component of the signal.

The pattern matcher 710 may receive an input from the DSP 215 of the TX210. The input from the DSP 215 may result from known DSP techniquesapplied in, for instance, upstream modules of the DSP 260. Such upstreammodules may comprise a slicer similar to the slicer 520 so that theinput from the DSP 215 is a hard signal. The pattern matcher 710 maycompare the hard signal to mapped levels, which may be based on anarbitrary scheme. The arbitrary scheme may have the same number oflevels as the modulation scheme, but use different levels, The patternmatcher 710 may then convert the hard signal to a matched signal basedon the comparison. The pattern matcher 710 may also calculate a patternindex by multiplying the first symbol in the first sequence of thesignal by the number of matched levels raised to the power of the symbolnumber, multiplying the second symbol in the first sequence of thesignal by the number of matched levels raised to the power of the symbolnumber, and so on for each symbol, then adding the quantities together.

The adjuster 720 may input a PD-LUT, for instance the PD-LUT 600, fromthe RX 240 in the first transceiver 205, which the RX 240 may havereceived from the TX 280 in the second transceiver 250. The adjuster 720may then look up in the PD-LUT the pattern index calculated by thepattern matcher 710, then determine the adjustment in the PD-LUTcorresponding to that pattern index. The adjuster 720 may then adjustthe center symbol of each sequence of the hard signal by the adjustment.

It is known that calculating an adjustment of the center symbol in asequence of a signal, then compensating that center symbol, may reduceimpairments. If, however, a sequence has an even number of symbols, thenthe center two symbols may be compensated. Similarly, symbols other thanthe center symbol or symbols may be compensated in other applications.

As an example, the pattern matcher 710 may input the following hardsignal:

(−3, −3, −1, 1, 3)   (7)

The pattern matcher 710 may match the hard signal (7) to a matchedsignal based on the four mapped levels, 0, 1, 2, and 3, to obtain thefollowing matched signal:

(0, 0, 1, 2, 3).   (8)

In the same way as described for the pattern matcher 530, the patternmatcher 710 may also calculate the pattern index of the matched signal(8) as follows:

(0×4 ⁰)+(0×4¹)+(1×4²)+(2×4³)+(3×4⁴)=912.   (9)

The adjuster 720 may then look up in the PD-LUT 600 the pattern index(9) and determine a corresponding adjustment for that pattern index. Asdescribed above and as shown in FIG. 6, 0.03 is the adjustmentcorresponding to the pattern index of 912. Accordingly, the adjuster 720may adjust the center symbol of the hard signal (7) by 0.3 to obtain thefollowing adjusted signal:

(−3, −3, −0.97, 1, 3).   (10)

Finally, the adjuster 720 may provide the adjusted signal (10) to theDSP 215. For instance, the adjuster 720 may provide the adjusted signal(10) to downstream modules of the DSP 215. Such downstream modules mayapply known DSP techniques.

FIG. 8 is a message sequence diagram illustrating iterative calibrationand compensation scheme 800 according to an embodiment of thedisclosure. The optical network 400 may implement the scheme 800.Specifically, the first transceiver 205 and the second transceiver 250may implement the scheme 800, though the same principles may applybetween any suitable transmitter and receiver.

At step 805, the first transceiver 205 may transmit a first signal tothe second transceiver 250. At step 810, the second transceiver 250 mayperform a first calibration, for instance in the calibrator 410, toproduce a PD-LUT, for instance the PD-LUT 600. The calibrator 410 mayperform the first calibration based on the first signal. At step 815,the second. transceiver 250 may transmit the PD-LUT 600 to the firsttransceiver 205. At step 820, the first transceiver 205 may perform afirst compensation, for instance in the compensator 420. For instance,the compensator 420 may compensate subsequent transmissions by applyingto those transmissions the adjustments in the PD-LUT 600. Steps 805 to820 may comprise a first iteration of calibration and compensation.

The first iteration may not, however, fully compensate the signals thatthe first transceiver 205 transmits. The scheme 800 may thereforecomprise additional iterations of calibration and compensation.Accordingly, at step 825, the first transceiver 205 may transmit asecond signal to the second transceiver 250. The second signal may becompensated based on the PD-LUT 600, At step 830, the calibrator 410 mayperform a second calibration to produce a PID-LUT Δ₂. The PD-LUT Δ₂ mayprovide adjustments to be added to the adjustments from the PD-LUT 600to form anew PD-LUT₂. For instance, for a pattern index of 912, thePD-LUT Δ₂ may provide an adjustment of 0.005 to add to the adjustment of0.03 in the PD-LUT 600 to form a new PD-LUT₂ with an adjustment of 0.035for a pattern index of 912. The calibrator 410 may perform the secondcalibration in the same manner that it performed the first calibration,except that the calibrator may do so based on the second signal. At step835, the second transceiver 250 may transmit the PD-LUT₂ to the firsttransceiver 205. At step 840, the compensator 420 may perform a secondcompensation. For instance, the compensator 420 may compensatesubsequent transmissions by applying to those transmissions theadjustments in the PD-LUT₂. Steps 825 to 840 may comprise a seconditeration of calibration and compensation.

The scheme 800 may comprise similar additional iterations of calibrationand compensation until an ith iteration at steps 845 to 860. I may beany positive integer. Each successive iteration may provide a finergranularity of compensation. The first transceiver 205, the secondtransceiver 250, or another component may request a first or subsequentiteration.

FIG. 9 is a graph 900 of a modeled BER for the optical network 400 inFIG. 4. As shown, the x-axis represents calibration and compensationiterations as constants, and the y-axis represents BER as constants orarbitrary units. Non-linearity of the RFA 225 may be modeled using theRapp model, which is well-known in the art and described in manysources, including in John Liebetreu, et al., “Proposed SystemImpairment Models,” IEEE 802.16 Broadband Wireless Access Working Group,Mar. 8, 2000, which is incorporated by reference. The graph 900 showsBERs for a pattern length of five and for different saturation voltages,which are represented as V_(S) and described in Rapp. V_(S) may beinversely proportional to the non-linearity of the RFA 225, The solidline may represent a linear RFA 225.

As can be seen, the BER may decrease for each successive iteration,though improvement may begin to level off around three iterations. AV_(S) of 0.75 volts (V) yields a relatively low BER, while lower V_(S)values yield relatively higher BERs. The successive iterations may notfully compensate the non-linearity, particularly for the lower V_(S)values. That inability to compensate may be due to the relatively shortpattern length of five used in this example, which may not fullycompensate for the patterning effects.

FIG. 10 is another graph 1000 of a modeled BER for the optical network400 in FIG. 4. As shown, the x-axis represents calibration andcompensation iterations as constants, and the y-axis represents BER asconstants or arbitrary units. Once again, the Rapp model may be used.Compared to the graph 900, however, the graph 1000 shows BERs for aV_(S) of 0.5 V, a pre-compensation dispersion at the DSP 215 of 300picoseconds (ps)/nanometer (nm), a post-compensation dispersion at theDSP 260 of −300 ps/nm, and different pattern lengths, which arerepresented as PL. Once again, the solid line may represent a linear RFA225.

As can be seen, a higher pattern length yields a lower BER, particularlyafter successive iterations. Once again, however, the BER improvementmay begin to level off around three iterations. A pattern length of ninemay nearly fully compensate the patterning effects due to a combinationof pre-compensation dispersion and RFA 225 non-linearity.

FIG. 11 is a graph 1100 of an experimental symbol constellation for theoptical network 400 in FIG. 4. FIG. 12 is another graph 1200 of anexperimental symbol constellation for the optical network 400 in FIG. 4.The graph 1100 is shown before applying the disclosed. calibration andcompensation, and the graph 1200 is shown after applying the disclosedcalibration and compensation. As shown, for both the graph 1100 and thegraph 1200, both the x-axis and the y-axis represent constants orarbitrary units. The graph 1100 and the graph 1200 are obtainedexperimentally based on the following:

-   -   polarization-multiplexed 16-QAM (PM-16Q AM) transmission;    -   36 gigabaud (Gbaud) transmission;    -   a polarization-multiplexed I and Q (PM-IQ) modulator;    -   driving signals for the modulators generated electrically from        eight-bit, four-channel, high-speed DACs with sampling rates up        to 65 Gbaud;    -   a 2¹⁵-1 pseudo-random bit sequence (PRBS);    -   Nyquist RRC pulse-shaping with a roll-off factor of 0.1;    -   detection of the signal by a polarized, diversified, coherent        detector;    -   recordation of the signal using a 50 Gbaud Tektronix real-time        digital sampling oscilloscope (DSO) with a 20 gigahertz (GHz)        electrical bandwidth; and    -   signal processing using an offline DSP code package comprising        an FDEQ, a TDEQ, and a CR module.

As can be seen, the symbols in the graph 1100 are grouped together in 16circles, but the circles are not neatly defined. In the graph 1200,however, the 16 circles are more neatly defined, compact, and equallyspaced apart. In other words, the symbols are more closely aligned withthe PM-16QAM grid, The experimental BER in FIG. 11 is 1.67e⁻⁴, while theexperimental BER in FIG. 12 is 6.3e⁻⁵, thus showing substantialimprovement in BER.

FIG. 13 is a graph 1300 of experimental OSNR versus BER for the opticalnetwork 400 in FIG, 4. As shown, the x-axis represents OSNR in decibels(dB), and the y-axis represents BER in constants or arbitrary units. Thegraph 1300 is based on a V_(G) of 2 V, where V_(G) is a voltage relatedto the RFA 225. The graph 1300 shows OSNR versus BER before applying thedisclosed calibration and compensation and after applying the disclosedcalibration and compensation. As can be seen, the disclosed calibrationand compensation may significantly decrease the BER, particularly as theOSNR increases.

FIG. 14 is a graph 1400 of experimental pattern length versus BER forthe optical network 400 in FIG. 4. As shown, the x-axis representpattern length in constants or arbitrary units, and the y-axisrepresents BER in constants or arbitrary units. The graph 1400 is basedon a single iteration of calibration and compensation. As can be seen,the BER may significantly decrease as the pattern length increases,though improvement may begin to level off around a pattern length offour to five. The BER may begin to decrease as the pattern lengthincreases beyond seven.

FIG. 15 is a flowchart illustrating a method 1500 of transmitterimpairment compensation according to an embodiment of the disclosure.The method 1500 may be implemented in the first transceiver 205, forinstance in the TX 210, At step 1510, a first optical signal may betransmitted. At step 1520, a first compensation may be received. Forinstance, the TX 210 may receive the PD-LUT 600 from the secondtransceiver 250, for instance from the RX 255. The first compensationmay be based on a pattern-dependent analysis of the first opticalsignal. At step 1530, a second optical signal may be compensated basedon the first compensation to form a first compensated optical signal.For instance, the compensator 420 may compensate the second opticalsignal based on the PD-LUT 600. At step 1540, the first compensatedoptical signal may be transmitted.

At least one embodiment is disclosed and variations, combinations,and/or modifications of the embodiment(s) and/or features of theembodiment(s) made by a person having ordinary skill in the art arewithin the scope of the disclosure. Alternative embodiments that resultfrom combining, integrating, and/or omitting features of theembodiment(s) are also within the scope of the disclosure. Wherenumerical ranges or limitations are expressly stated, such expressranges or limitations may be understood to include iterative ranges orlimitations of like magnitude falling within the expressly stated rangesor limitations (e.g., from about 1 to about 10 includes, 2, 3, 4, etc.;greater than 0.10 includes 0.11, 0.12, 0.13, etc.). For example,whenever a numerical range with a lower limit, R₁, and an upper limit,R_(u), is disclosed, any number falling within the range is specificallydisclosed. In particular, the following numbers within the range arespecifically disclosed: R=R₁+k*(R_(u)−R₁), wherein k is a variableranging from 1 percent to 100 percent with a 1 percent increment, i.e.,k is 1 percent, 2 percent, 3 percent, 4 percent, 5 percent, 50 percent,51 percent, 52 percent, 95 percent, 96 percent, 97 percent, 98 percent,99 percent, or 100 percent. Moreover, any numerical range defined by twoR numbers as defined in the above is also specifically disclosed. Theuse of the term “about” means +/−10% of the subsequent number, unlessotherwise stated. Use of the term “optionally” with respect to anyelement of a claim means that the element is required, or alternatively,the element is not required, both alternatives being within the scope ofthe claim, Use of broader terms such as comprises, includes, and havingmay be understood to provide support for narrower terms such asconsisting of, consisting essentially of, and comprised substantiallyof. Accordingly, the scope of protection is not limited by thedescription set out above but is defined by the claims that follow, thatscope including all equivalents of the subject matter of the claims.Each and every claim is incorporated as further disclosure into thespecification and the claims are embodiment(s) of the presentdisclosure. The discussion of a reference in the disclosure is not anadmission that it is prior art, especially any reference that has apublication date after the priority date of this application. Thedisclosure of all patents, patent applications, and publications citedin the disclosure are hereby incorporated by reference, to the extentthat they provide exemplary, procedural, or other details supplementaryto the disclosure.

While several embodiments have been provided in the present disclosure,it may be understood that the disclosed systems and methods might beembodied in many other specific forms without departing from the spiritor scope of the present disclosure. The present examples are to beconsidered as illustrative and not restrictive, and the intention is notto be limited to the details given herein. For example, the variouselements or components may be combined or integrated in another systemor certain features may be omitted, or not implemented.

In addition, techniques, systems, subsystems, and methods described andillustrated in the various embodiments as discrete or separate may becombined or integrated with other systems, modules, techniques, ormethods without departing from the scope of the present disclosure.Other items shown or discussed as coupled or directly coupled orcommunicating with each other may be indirectly coupled or communicatingthrough some interface, device, or intermediate component whetherelectrically, mechanically, or otherwise. Other examples of changes,substitutions, and alterations are ascertainable by one skilled in theart and may be made without departing from the spirit and scopedisclosed herein.

What is claimed is:
 1. An optical transmitter comprising: a digitalsignal processor (DSP) comprising a compensator; a digital-to-analogconverter (DAC) coupled to the DSP; a radio frequency amplifier (RFA)coupled to the DAC; and an electrical-to-optical converter (EOC) coupledto the RFA.
 2. The optical transmitter of claim 1, wherein thecompensator comprises: a pattern matcher; and an adjuster coupled to thepattern matcher.
 3. The optical transmitter of claim 2, wherein thecompensator is configured to compensate a signal based on a compensationcalculated outside the optical transmitter.
 4. The optical transmitterof claim 2, wherein the compensation is a pattern-dependent look-uptabled (PD-LUT).
 5. An optical receiver comprising: anoptical-to-electrical converter (OEC); an analog-to-digital converter(ADC) coupled to the OEC; and a digital signal processor (DSP) coupledto the ADC and comprising a calibrator.
 6. The optical receiver of claim5, wherein the calibrator comprises a pattern-dependent look-up table(PD-LUT) generator.
 7. The optical receiver of claim 6, wherein thecalibrator further comprises: a multiple-input and multiple-output(MEMO) time-domain equalizer (TDEQ) and carrier recovery (CR) module; aslicer coupled to the MIMO TDEQ and CR module; a pattern matcher coupledto the slicer; a mean calculator coupled to the pattern matcher; and anadjustment calculator coupled to the mean calculator and the PD-LUTgenerator.
 8. The optical receiver of claim 7, wherein the PD-LUTgenerator is configured to generate a first PD-LUT based on a firstsignal generated outside the optical receiver.
 9. The optical receiverof claim 8, wherein the PD-LUT generator is configured to generate aPD-LUT A based on a second signal generated outside the opticalreceiver, wherein Δ represents an increment to the first PD-LUT, andwherein the second signal is compensated based on the first PD-LUT. 10.The optical receiver of claim 9, wherein the PD-LUT generator isconfigured to generate a second PD-LUT by adding values of the PD-LUT Δto values of the first PD-LUT.